package asd.geometry;



/**
 * Implementation of a 4x4 matrix suited for use in a 2D and 3D
 * graphics rendering engine.
 * 
 * @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
 */   
public class Matrix4x4 
{
  private double[]  m_;  // of 16


  
  /**
   * Construct a 4x4 identity matrix.
   */
  public Matrix4x4()
  {
    initialize();
    setIdentity();
  }

  

  /**
   * Construct a 4x4 matrix with the specified element values.
   * 
   * @param m  Array of 16 matrix elements, m00, m01, etc.
   */
  public Matrix4x4 (double[] m)
  {
    initialize();
    set (m);
  }

  

  /**
   * Constrauct a 4x4 matrix as a copy of the specified matrix.
   * 
   * @param matrix  Matrix to copy.
   */
  public Matrix4x4 (Matrix4x4 matrix)
  {
    initialize();
    set (matrix);
  }

  

  /**
   * Construct a 4x4 matrix with the specified values.
   * 
   * @param m00  Value of element m[0,0].
   * @param m01  Value of element m[0,1].
   * @param m02  Value of element m[0,2].
   * @param m03  Value of element m[0,3].
   * @param m10  Value of element m[1,0].
   * @param m11  Value of element m[1,1].
   * @param m12  Value of element m[1,2].
   * @param m13  Value of element m[1,3].
   * @param m20  Value of element m[2,0].
   * @param m21  Value of element m[2,1].
   * @param m22  Value of element m[2,2].
   * @param m23  Value of element m[2,3].
   * @param m30  Value of element m[3,0].
   * @param m31  Value of element m[3,1].
   * @param m32  Value of element m[3,2].
   * @param m33  Value of element m[3,3].
   */
  public Matrix4x4 (double m00, double m01, double m02, double m03,
                    double m10, double m11, double m12, double m13,
                    double m20, double m21, double m22, double m23,
                    double m30, double m31, double m32, double m33)
  {
    initialize();
    set (m00, m01, m02, m03,
         m10, m11, m12, m13,
         m20, m21, m22, m23,
         m30, m31, m32, m33);
  }
  


  /**
   * Initialize the matrix.
   */
  private void initialize()
  {
    m_ = new double[16];
  }

  

  /**
   * Make an identity matrix out of this 4x4 matrix.
   */
  public void setIdentity()
  {
    for (int i=0; i<4; i++)
      for (int j=0; j<4; j++)
        m_[i*4 + j] = i == j ? 1.0 : 0.0;
  }



  /**
   * Set the value of this 4x4matrix according to the specified
   * matrix
   *
   * @param matrix  Matrix to copy.
   */
  public void set (Matrix4x4 matrix)
  {
    for (int i=0; i<16; i++)
      m_[i] = matrix.m_[i];
  }
  

  
  /**
   * Set the values of this 4x4 matrix.
   * 
   * @param m  Array of 16 matrix elements, m00, m01, etc.
   */
  public void set (double[] m)
  {
    for (int i=0; i<16; i++)
      m_[i] = m[i];
  }


  
  /**
   * Set the values of this 4x4 matrix.
   * 
   * @param m00  Value of element m[0,0].
   * @param m01  Value of element m[0,1].
   * @param m02  Value of element m[0,2].
   * @param m03  Value of element m[0,3].
   * @param m10  Value of element m[1,0].
   * @param m11  Value of element m[1,1].
   * @param m12  Value of element m[1,2].
   * @param m13  Value of element m[1,3].
   * @param m20  Value of element m[2,0].
   * @param m21  Value of element m[2,1].
   * @param m22  Value of element m[2,2].
   * @param m23  Value of element m[2,3].
   * @param m30  Value of element m[3,0].
   * @param m31  Value of element m[3,1].
   * @param m32  Value of element m[3,2].
   * @param m33  Value of element m[3,3].
   */
  public void set (double m00, double m01, double m02, double m03,
                   double m10, double m11, double m12, double m13,
                   double m20, double m21, double m22, double m23,
                   double m30, double m31, double m32, double m33)
  {
    m_[0]  = m00;
    m_[1]  = m01;
    m_[2]  = m02;
    m_[3]  = m03;  
  
    m_[4]  = m10;
    m_[5]  = m11;
    m_[6]  = m12;
    m_[7]  = m13;  

    m_[8]  = m20;
    m_[9]  = m21;
    m_[10] = m22;
    m_[11] = m23;  

    m_[12] = m30;
    m_[13] = m31;
    m_[14] = m32;
    m_[15] = m33;  
  }

  

  /**
   * Return the values of this 4x4 matrix.
   * 
   * @return  Array ov values: m00, m01, etc.
   */
  public double[] get()
  {
    return m_;
  }
  

  
  /**
   * Check if this 4x4 matrix equals the specified object.
   * 
   * @param object  Object to check.
   * @return        True if the two are equal, false otherwise.
   * @throws        ClassCastException if object is not of type Matrix4x4.
   */
  public boolean equals (Object object)
  {
    Matrix4x4 matrix = (Matrix4x4) object;
    
    for (int i=0; i<16; i++)
      if (m_[i] != matrix.m_[i]) return false;
    return true;
  }

  

  /**
   * Return matrix element [i,j].
   * 
   * @param i  Row of element to get (first row is 0).
   * @param j  Column of element to get (first column is 0).
   * @return   Element at specified position.
   * @throws   ArrayOutOfBoundsException
   */
  public double getElement (int i, int j)
  {
    return m_[i*4 + j];  
  }

  

  /**
   * Set specified matrix element.
   * 
   * @param i      Row of element to set (first row is 0).
   * @param j      Column of element to set (first column is 0).
   * @param value  New element value.
   * @throws       ArrayOutOfBoundsException
   */
  public void setElement (int i, int j, double value)
  {
    m_[i*4 + j] = value;
  }
  


  /**
   * Add the specified 4x4 matrix to this matrix.
   * 
   * @param matrix  Matrix to add.
   */
  public void add (Matrix4x4 matrix)
  {
    for (int i=0; i<4; i++)
      for (int j=0; j<4; j++)
        m_[i*4 + j] += matrix.m_[i*4 + j];
  }


  
  /**
   * Add two matrices and return the result matrix.
   * 
   * @param m1  First matrix to add.
   * @param m2  Second matrix to add.
   * @return    Sum m1 + m2.
   */
  public static Matrix4x4 add (Matrix4x4 m1, Matrix4x4 m2)
  {
    Matrix4x4 m = new Matrix4x4 (m1);
    m.add (m2);
    return m;
  }
  
  
  
  /**
   * Multiply this 4x4 matrix with the specified matrix and
   * store the result in this 4x4 matrix.
   * 
   * @param matrix  Matrix to multiply with.
   */
  public void multiply (Matrix4x4 matrix)
  {
    Matrix4x4 product = new Matrix4x4();
    
    for (int i = 0; i < 16; i += 4) {
      for (int j = 0; j < 4; j++) {
        product.m_[i + j] = 0.0;
        for (int k = 0; k < 4; k++)
          product.m_[i + j] += m_[i + k] * matrix.m_[k*4 + j];
      }
    }

    set (product);
  }


  
  /**
   * Multiply two matrices and return the result matrix.
   * 
   * @param m1  First matrix to multiply.
   * @param m2  Second matrix to multiply.
   * @return    Product m1 * m2.
   */
  public static Matrix4x4 multiply (Matrix4x4 m1, Matrix4x4 m2)
  {
    Matrix4x4 m = new Matrix4x4 (m1);
    m.multiply (m2);
    return m;
  }

  

  /**
   * Multiply this 4x4 matrix with the specified vector.
   * 
   * @param vector4  Vector to multiply with.
   * @return         Result of operation.
   */
  public Vector4 multiply (Vector4 vector4)
  {
    Vector4  product = new Vector4();

    for (int i = 0; i < 4; i++) {
      double value = 0.0;
      for (int j = 0; j < 4; j++)
        value += getElement(i, j) * vector4.getElement (j);
      product.setElement (i, value);
    }

    return product;
  }
  


  /**
   * Transform one coordinate using this 4x4 matrix.
   * 
   * @param point  [x0,y0,z0]
   * @return       Result of operation: [x0',y0',z0']
   */
  public double[] transformPoint (double[] point)
  {
    double[]  result = new double[3];

    result[0] = point[0] * m_[0]  +
                point[1] * m_[4]  +
                point[2] * m_[8]  + m_[12];
    
    result[1] = point[0] * m_[1]  +
                point[1] * m_[5]  +
                point[2] * m_[9]  + m_[13];
    
    result[2] = point[0] * m_[2]   +
                point[1] * m_[6]   +
                point[2] * m_[10]  + m_[14];

    return result;
  }
  


  /**
   * Transform a set of 3D coordinates using this 4x4 matrix.
   * The result of the operation is put back in the original array.
   * 
   * @param point  Points to transform [x0,y0,z0,x1,y1,z1,...]
   */
  public void transformPoints (double[] points)
  {
    for (int i = 0; i < points.length; i += 3) {
      double x = points[i + 0] * m_[0]  +
                 points[i + 1] * m_[4]  +
                 points[i + 2] * m_[8]  + m_[12];

      double y = points[i + 0] * m_[1]  +
                 points[i + 1] * m_[5]  +
                 points[i + 2] * m_[9]  + m_[13];

      double z = points[i + 0] * m_[2]   +
                 points[i + 1] * m_[6]   +
                 points[i + 2] * m_[10]  + m_[14];

      points[i + 0] = x;
      points[i + 1] = y;
      points[i + 2] = z;            
    }
  }


  
  /**
   * Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
   * The result of the operation is put back in the original array
   * rounded to the nearest integer.
   * 
   * @param points  Points to transform [x0,y0,x1,y1,...].
   */
  public void transformXyPoints (double[] points)
  {
    for (int i = 0; i < points.length; i += 2) {
      double x = points[i + 0] * m_[0]  +
                 points[i + 1] * m_[4]  + m_[12];

      double y = points[i + 0] * m_[1]  +
                 points[i + 1] * m_[5]  + m_[13];

      points[i + 0] = x;
      points[i + 1] = y;
    }
  }

  
  
  /**
   * Transform a set of 3D coordinates using this 4x4 matrix.
   * The result of the operation is put back in the original array.
   * 
   * @param points  Points to transform [x0,y0,z0,x1,y1,z1,...].
   */
  public void transformPoints (int[] points)
  {
    for (int i = 0; i < points.length; i += 3) {
      double x = points[i + 0] * m_[0]  +
                 points[i + 1] * m_[4]  +
                 points[i + 2] * m_[8]  + m_[12];
      
      double y = points[i + 0] * m_[1]  +
                 points[i + 1] * m_[5]  +
                 points[i + 2] * m_[9]  + m_[13];
      
      double z = points[i + 0] * m_[2]  +
                 points[i + 1] * m_[6]  +
                 points[i + 2] * m_[10] + m_[14];

      points[i + 0] = (int) Math.round (x);
      points[i + 1] = (int) Math.round (y);
      points[i + 2] = (int) Math.round (z);            
    }
  }


  
  /**
   * Transform a set of 2D (x,y) coordinates using this 4x4 matrix.
   * The result of the operation is put back in the original array
   * rounded to the nearest integer.
   * 
   * @param points  Points to transform [x0,y0,x1,y1,...].
   */
  public void transformXyPoints (int[] points)
  {
    for (int i = 0; i < points.length; i += 2) {
      double x = points[i + 0] * m_[0] +
                 points[i + 1] * m_[4] + m_[12];
      
      double y = points[i + 0] * m_[1]  +
                 points[i + 1] * m_[5]  + m_[13];

      points[i + 0] = (int) Math.round (x);
      points[i + 1] = (int) Math.round (y);
    }
  }



  /**
   * Apply specified translation to this 4x4 matrix.
   * 
   * @param dx  x translation.
   * @param dy  y translation.
   * @param dz  z translation.
   */
  public void translate (double dx, double dy, double dz)
  {
    Matrix4x4  translationMatrix = new Matrix4x4();

    translationMatrix.setElement (3, 0, dx);
    translationMatrix.setElement (3, 1, dy);
    translationMatrix.setElement (3, 2, dz);
    
    multiply (translationMatrix);
  }
  


   /**
   * Apply specified XY translation to this 4x4 matrix.
   * 
   * @param dx  x translation.
   * @param dy  y translation.
   */
  public void translate (double dx, double dy)
  {
    translate (dx, dy, 0.0);
  }



  /**
   * Apply rotation around X axis to this matrix.
   * 
   * @param angle  Angle to rotate [radians].
   */
  public void rotateX (double angle)
  {
    Matrix4x4 rotationMatrix = new Matrix4x4();

    double cosAngle = Math.cos (angle);
    double sinAngle = Math.sin (angle);  

    rotationMatrix.setElement (1, 1,  cosAngle);
    rotationMatrix.setElement (1, 2,  sinAngle);
    rotationMatrix.setElement (2, 1, -sinAngle);
    rotationMatrix.setElement (2, 2,  cosAngle);

    multiply (rotationMatrix);
  }



  /**
   * Apply rotation around Y axis to this matrix.
   * 
   * @param angle  Angle to rotate [radians].
   */
  public void rotateY (double angle)
  {
    Matrix4x4 rotationMatrix = new Matrix4x4();

    double cosAngle = Math.cos (angle);
    double sinAngle = Math.sin (angle);  

    rotationMatrix.setElement (0, 0,  cosAngle);
    rotationMatrix.setElement (0, 2, -sinAngle);
    rotationMatrix.setElement (2, 0,  sinAngle);
    rotationMatrix.setElement (2, 2,  cosAngle);

    multiply (rotationMatrix);
  }



  /**
   * Apply rotation around z axis to this matrix.
   * 
   * @param angle  Angle to rotate [radians].
   */
  public void rotateZ (double angle)
  {
    Matrix4x4 rotationMatrix = new Matrix4x4();

    double cosAngle = Math.cos (angle);
    double sinAngle = Math.sin (angle);  

    rotationMatrix.setElement (0, 0,  cosAngle);
    rotationMatrix.setElement (0, 1,  sinAngle);
    rotationMatrix.setElement (1, 0, -sinAngle);
    rotationMatrix.setElement (1, 1,  cosAngle);

    multiply (rotationMatrix);
  }


      
  /**
   * Apply rotation around an arbitrary axis.
   *
   * Ref: http://www.swin.edu.au/astronomy/pbourke/geometry/rotate/
   * (but be aware of errors, corrected here)
   *
   * @param angle  Angle to rotate [radians]
   * @param p0     First point defining the axis (x,y,z)
   * @param p1     Second point defining the axis (x,y,z)
   */
  public void rotate (double angle, double[] p0, double[] p1)
  {
    // Represent axis of rotation by a unit vector [a,b,c]
    double a = p1[0] - p0[0];
    double b = p1[1] - p0[1];
    double c = p1[2] - p0[2];  
    
    double length = Math.sqrt (a*a + b*b + c*c);

    a /= length;
    b /= length;
    c /= length;  

    double d = Math.sqrt (b*b + c*c);

    // Coefficients used for step 2 matrix
    double e = d == 0.0 ? 1.0 : c / d;
    double f = d == 0.0 ? 0.0 : b / d;  
  
    // Coefficients used for the step 3 matrix
    double k = d;
    double l = a;
    
    // Coefficients for the step 5 matrix (inverse of step 3)
    double m = d / (a*a + d*d);
    double n = a / (a*a + d*d);  
    
    // Coefficients for the step 4 matrix
    double cosAngle = Math.cos (angle);
    double sinAngle = Math.sin (angle);  
    
    //
    // Step 1
    //
    Matrix4x4  step1 = new Matrix4x4();
    step1.setElement (3, 0, -p0[0]);
    step1.setElement (3, 1, -p0[1]);
    step1.setElement (3, 2, -p0[2]);

    //
    // Step 2
    //
    Matrix4x4  step2 = new Matrix4x4();
    step2.setElement (1, 1,  e);
    step2.setElement (1, 2,  f);
    step2.setElement (2, 1, -f);
    step2.setElement (2, 2,  e);      

    //
    // Step 3
    //
    Matrix4x4  step3 = new Matrix4x4();
    step3.setElement (0, 0,  k);
    step3.setElement (0, 2,  l);
    step3.setElement (2, 0, -l);
    step3.setElement (2, 2,  k);
    
    //
    // Step 4
    //
    Matrix4x4  step4 = new Matrix4x4();
    step4.setElement (0, 0,  cosAngle);
    step4.setElement (0, 1,  sinAngle);
    step4.setElement (1, 0, -sinAngle);
    step4.setElement (1, 1,  cosAngle);
    
    //
    // Step 5 (inverse of step 3)
    //
    Matrix4x4  step5 = new Matrix4x4();
    step5.setElement (0, 0,  m);
    step5.setElement (0, 2, -n);
    step5.setElement (2, 0,  n);
    step5.setElement (2, 2,  m);
    
    //
    // Step 6 (inverse of step 2)
    //
    Matrix4x4  step6 = new Matrix4x4();
    step6.setElement (1, 1,  e);
    step6.setElement (1, 2, -f);
    step6.setElement (2, 1,  f);
    step6.setElement (2, 2,  e);      
    
    //
    // Step 7 (inverse of step 1)
    //
    Matrix4x4  step7 = new Matrix4x4();
    step7.setElement (3, 0, p0[0]);
    step7.setElement (3, 1, p0[1]);
    step7.setElement (3, 2, p0[2]);

    multiply (step1);
    multiply (step2);
    multiply (step3);
    multiply (step4);
    multiply (step5);
    multiply (step6);
    multiply (step7);
  }


  
  /**
   * Apply scaling (relative to origo) to this 4x4 matrix.
   * 
   * @param xScale  Scaling in x direction.
   * @param yScale  Scaling in y direction.
   * @param zScale  Scaling in z direction.
   */
  public void scale (double xScale, double yScale, double zScale)
  {
    Matrix4x4  scalingMatrix = new Matrix4x4();

    scalingMatrix.setElement (0, 0, xScale);
    scalingMatrix.setElement (1, 1, yScale);
    scalingMatrix.setElement (2, 2, zScale);  
    
    multiply (scalingMatrix);
  }


  
  /**
   * Apply scaling relative to a fixed point to this 4x4 matrix.
   * 
   * @param xScale      Scaling in x direction.
   * @param yScale      Scaling in y direction.
   * @param zScale      Scaling in z direction.
   * @param fixedPoint  Scaling origo.
   */
  public void scale (double xScale, double yScale, double zScale,
                     double[] fixedPoint)
  {
    Matrix4x4 step1 = new Matrix4x4();
    step1.translate (-fixedPoint[0], -fixedPoint[1], -fixedPoint[2]);

    Matrix4x4 step2 = new Matrix4x4();
    step2.scale (xScale, yScale, zScale);
  
    Matrix4x4 step3 = new Matrix4x4();
    step3.translate (fixedPoint[0], fixedPoint[1], fixedPoint[2]);

    multiply (step1);
    multiply (step2);
    multiply (step3);
  }
  


  /**
   * Invert this 4x4 matrix.
   */
  public void invert()
  {
    double[] tmp = new double[12];
    double[] src = new double[16];
    double[] dst = new double[16];  

    // Transpose matrix
    for (int i = 0; i < 4; i++) {
      src[i +  0] = m_[i*4 + 0];
      src[i +  4] = m_[i*4 + 1];
      src[i +  8] = m_[i*4 + 2];
      src[i + 12] = m_[i*4 + 3];
    }

    // Calculate pairs for first 8 elements (cofactors) 
    tmp[0] = src[10] * src[15];
    tmp[1] = src[11] * src[14];
    tmp[2] = src[9]  * src[15];
    tmp[3] = src[11] * src[13];
    tmp[4] = src[9]  * src[14];
    tmp[5] = src[10] * src[13];
    tmp[6] = src[8]  * src[15];
    tmp[7] = src[11] * src[12];
    tmp[8] = src[8]  * src[14];
    tmp[9] = src[10] * src[12];
    tmp[10] = src[8] * src[13];
    tmp[11] = src[9] * src[12];
    
    // Calculate first 8 elements (cofactors)
    dst[0]  = tmp[0]*src[5] + tmp[3]*src[6] + tmp[4]*src[7];
    dst[0] -= tmp[1]*src[5] + tmp[2]*src[6] + tmp[5]*src[7];
    dst[1]  = tmp[1]*src[4] + tmp[6]*src[6] + tmp[9]*src[7];
    dst[1] -= tmp[0]*src[4] + tmp[7]*src[6] + tmp[8]*src[7];
    dst[2]  = tmp[2]*src[4] + tmp[7]*src[5] + tmp[10]*src[7];
    dst[2] -= tmp[3]*src[4] + tmp[6]*src[5] + tmp[11]*src[7];
    dst[3]  = tmp[5]*src[4] + tmp[8]*src[5] + tmp[11]*src[6];
    dst[3] -= tmp[4]*src[4] + tmp[9]*src[5] + tmp[10]*src[6];
    dst[4]  = tmp[1]*src[1] + tmp[2]*src[2] + tmp[5]*src[3];
    dst[4] -= tmp[0]*src[1] + tmp[3]*src[2] + tmp[4]*src[3];
    dst[5]  = tmp[0]*src[0] + tmp[7]*src[2] + tmp[8]*src[3];
    dst[5] -= tmp[1]*src[0] + tmp[6]*src[2] + tmp[9]*src[3];
    dst[6]  = tmp[3]*src[0] + tmp[6]*src[1] + tmp[11]*src[3];
    dst[6] -= tmp[2]*src[0] + tmp[7]*src[1] + tmp[10]*src[3];
    dst[7]  = tmp[4]*src[0] + tmp[9]*src[1] + tmp[10]*src[2];
    dst[7] -= tmp[5]*src[0] + tmp[8]*src[1] + tmp[11]*src[2];
    
    // Calculate pairs for second 8 elements (cofactors)
    tmp[0]  = src[2]*src[7];
    tmp[1]  = src[3]*src[6];
    tmp[2]  = src[1]*src[7];
    tmp[3]  = src[3]*src[5];
    tmp[4]  = src[1]*src[6];
    tmp[5]  = src[2]*src[5];
    tmp[6]  = src[0]*src[7];
    tmp[7]  = src[3]*src[4];
    tmp[8]  = src[0]*src[6];
    tmp[9]  = src[2]*src[4];
    tmp[10] = src[0]*src[5];
    tmp[11] = src[1]*src[4];

    // Calculate second 8 elements (cofactors)
    dst[8]   = tmp[0] * src[13]  + tmp[3] * src[14]  + tmp[4] * src[15];
    dst[8]  -= tmp[1] * src[13]  + tmp[2] * src[14]  + tmp[5] * src[15];
    dst[9]   = tmp[1] * src[12]  + tmp[6] * src[14]  + tmp[9] * src[15];
    dst[9]  -= tmp[0] * src[12]  + tmp[7] * src[14]  + tmp[8] * src[15];
    dst[10]  = tmp[2] * src[12]  + tmp[7] * src[13]  + tmp[10]* src[15];
    dst[10] -= tmp[3] * src[12]  + tmp[6] * src[13]  + tmp[11]* src[15];
    dst[11]  = tmp[5] * src[12]  + tmp[8] * src[13]  + tmp[11]* src[14];
    dst[11] -= tmp[4] * src[12]  + tmp[9] * src[13]  + tmp[10]* src[14];
    dst[12]  = tmp[2] * src[10]  + tmp[5] * src[11]  + tmp[1] * src[9];
    dst[12] -= tmp[4] * src[11]  + tmp[0] * src[9]   + tmp[3] * src[10];
    dst[13]  = tmp[8] * src[11]  + tmp[0] * src[8]   + tmp[7] * src[10];
    dst[13] -= tmp[6] * src[10]  + tmp[9] * src[11]  + tmp[1] * src[8];
    dst[14]  = tmp[6] * src[9]   + tmp[11]* src[11]  + tmp[3] * src[8];
    dst[14] -= tmp[10]* src[11 ] + tmp[2] * src[8]   + tmp[7] * src[9];
    dst[15]  = tmp[10]* src[10]  + tmp[4] * src[8]   + tmp[9] * src[9];
    dst[15] -= tmp[8] * src[9]   + tmp[11]* src[10]  + tmp[5] * src[8];

    // Calculate determinant
    double det = src[0]*dst[0] + src[1]*dst[1] + src[2]*dst[2] + src[3]*dst[3];
    
    // Calculate matrix inverse
    det = 1.0 / det;
    for (int i = 0; i < 16; i++)
      m_[i] = dst[i] * det;
  }


  
  /**
   * Return the inverse of the specified matrix.
   * 
   * @param matrix  Matrix to finr the inverse of.
   * @return        Inverse of the specified matrix.
   */
  public static Matrix4x4 inverse (Matrix4x4 matrix)
  {
    Matrix4x4 m = new Matrix4x4 (matrix);
    m.invert();
    return m;
  }
    
  
  
  /**
   * Solve the A x = b equation, where A is this 4x4 matrix, b is the
   * specified result vector and the returned vector is the unknown x.
   *
   * @param vector  Result vector
   * @return        Unknown vector.
   */
  public Vector4 solve (Vector4 vector)
  {
    Matrix4x4 inverse = new Matrix4x4 (this);
    inverse.invert();
    Vector4 result = inverse.multiply (vector);
    return result;
  }


  
  /**
   * Make this 4x4 matrix a world-2-device transformation matrix.
   * <p>
   * The world system is defined as follows:
   *
   * <pre>
   *        w2 o 
   *           |
   *           |
   *           |
   *        w0 o-------o w1
   * <pre>
   * <p>
   * Each point is defined with x,y,z so this system may in effect be
   * arbitrary oriented in space, and may include sharing.
   * <p>
   * The device system is defined as follows:
   *
   * <pre>
   *             width
   *     x0,y0 o-------o
   *           |
   *    height |
   *           |
   *           o
   * </pre>
   * <p>
   * The matrix maps w2 to (x0,y0), w0 to the lower left corner of the
   * device rectangle, and w1 to the lower right corner of the device
   * rectangle.
   *
   * @param w0      x,y,z coordinate of first world position.
   * @param w1      x,y,z coordinate of second world position.
   * @param w2      x,y,z coordinate of third world position.
   * @param x0      X coordinate of upper left corner of device.
   * @param y0      Y coordinate of upper left corner of device.
   * @param width   Width of device
   * @param height  Height of device.
   */
  public void setWorld2DeviceTransform (double[] w0, double[] w1, double[] w2,
                                        int x0, int y0, int width, int height)
  {
    setIdentity();
    
    double[] x = new double[4];
    double[] y = new double[4];
    double[] z = new double[4];

    // Make direction vectors for new system
    x[0] = w2[0];          y[0] = w2[1];          z[0] = w2[2];
    x[1] = w1[0] - w0[0];  y[1] = w1[1] - w0[1];  z[1] = w1[2] - w0[2];
    x[2] = w0[0] - w2[0];  y[2] = w0[1] - w2[1];  z[2] = w0[2] - w2[2];

    x[3] = y[1]*z[2] - z[1]*y[2];
    y[3] = z[1]*x[2] - x[1]*z[2];
    z[3] = x[1]*y[2] - y[1]*x[2];

    // Normalize new z-vector, in case someone needs
    // new z-value in addition to device coordinates */
    double length = Math.sqrt (x[3]*x[3] + y[3]*y[3] + z[3]*z[3]); 
    x[3] /= length;
    y[3] /= length;
    z[3] /= length;

    // Translate back to new origin                                
    translate (-x[0], -y[0], -z[0]);

    // Multiply with inverse of definition of new coordinate system
    double a = y[2]*z[3] - z[2]*y[3];
    double b = z[1]*y[3] - y[1]*z[3];
    double c = y[1]*z[2] - z[1]*y[2];
    
    double det = x[1]*a + x[2]*b + x[3]*c;

    double[] m = new double[16];

    m[0]  = a / det; 
    m[1]  = b / det; 
    m[2]  = c / det; 
    m[3]  = 0.0;

    m[4]  = (x[3]*z[2] - x[2]*z[3]) / det;   
    m[5]  = (x[1]*z[3] - x[3]*z[1]) / det; 
    m[6]  = (z[1]*x[2] - x[1]*z[2]) / det;               
    m[7]  = 0.0;

    m[8]  = (x[2]*y[3] - x[3]*y[2]) / det;  
    m[9]  = (y[1]*x[3] - x[1]*y[3]) / det;  
    m[10] = (x[1]*y[2] - y[1]*x[2]) / det;
    m[11] = 0.0;

    m[12] = 0.0; 
    m[13] = 0.0; 
    m[14] = 0.0; 
    m[15] = 1.0;

    Matrix4x4 matrix = new Matrix4x4 (m);
    multiply (matrix);

    // Scale according to height and width of viewport
    matrix.setIdentity();
    matrix.setElement (0, 0, width);
    matrix.setElement (1, 1, height);
    multiply (matrix);

    // Translate according to origin of viewport
    matrix.setIdentity();
    matrix.setElement (3, 0, x0);
    matrix.setElement (3, 1, y0);
    multiply (matrix);
  }
  


  /**
   * Create a string representation of this matrix.
   * 
   * @return  String representing this matrix.
   */
  public String toString()
  {
    String string = new String();

    for (int i=0; i<4; i++) {
      for (int j=0; j<4; j++)
        string += getElement(i,j) + " ";
      string += '\n';
    }

    return string;
  }
}
